English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the model Poisson problem $-\Delta u = f \in \Omega$, $u = g$ on$\pa \Omega$, where $ \Omega $ is a bounded polyhedral domain in $\RR^n$. Theobjective of the paper is twofold. The first objective is to review the wellposedness and the regularity of our model problem using appropriate weightedspaces for the data and the solution. We use these results to derive the domainof the Laplace operator with zero boundary conditions on a concave domain,which seems not to have been fully investigated before. We also mention someextensions of our results to interface problems for the Elasticity equation.The second objective is to illustrate how anisotropic weighted regularityresults for the Laplace operator in 3D are used in designing efficient finiteelement discretizations of elliptic boundary value problems, with the focus onthe efficient discretization of the Poisson problem on polyhedral domains in$\RR^3$, following {\em Numer. Funct. Anal. Optim.}, 28(7-8):775--824, 2007.The anisotropic weighted regularity results described and used in the secondpart of the paper are a consequence of the well-posedness results in(isotropically) weighted Sobolev spaces described in the first part of thepaper. The paper is based on the talk by the last named author at the Congressof Romanian Mathematicians, Brasov 2011, and is largely a survey paper.

Anisotropic regularity and optimal rates of convergence for the Finite Element Method on three dimensional polyhedral domains